In recent years the pressure to cut costs in intensive care and coronary care units has lead to the use of monitoring apparatus having bedside units for deriving physiological data for each patient and means for displaying that data at the bedside where it was derived and at a central station. It has also been possible to view data at one bedside that is derived at another. If it were necessary to analyze the real time data for each patient all of the time, the number of nurses would not be reduced significantly so that it has been customary to provide such monitoring systems with computers or microprocessors that are programmed with algorithms for analyzing the data for each patient to render a "yellow" alert when a situation of some concern but which is not life threatening exists and a "red" alert when a situation exists that may be life threatening. Past practice has been to sequentially record on paper at the central station all of the data occurring during either of these alerts so that it can be subsequently reviewed by a physician. Because the algorithms are usually designed to give alerts in borderline situations, the amount of data that must be reviewed by the physician can be excessive and much of it is redundant. Furthermore, if a physician or other clinician is at the bedside and desires past data, it is necessary to obtain the paper recordings. This requires a lot of pasting and cutting in order that the strips for a given patient may be separated from the others. A significant inconvenience of prior monitoring systems is that the control of what data is to be displayed and the condition under which it is to be displayed is at the central station or the bedside.